James Owen Weatherall

On (Some) Explanations in Physics

I offer an explanation of why inertial and gravitational mass are equal in Newtonian gravitation. I then argue that this is an example of a kind of explanation that is not captured by standard philosophical accounts of scientific explanation. Moreover, this form of explanation is particularly important, at least in physics, because demands for this kind of explanation are used to motivate and shape research into the next generation of physical theories. I suggest that explanations of the sort I describe reveal something important about one way in which physical theories may be related diachronically.

Regarding the "Hole Argument"

I argue that the hole argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the hole argument is blocked. 1. Introduction 2. A Warmup Exercise 3. The Hole Argument 4. An Argument from Classical Spacetime Theory 5. The Hole Argument Revisited 1. Introduction 2. A Warmup Exercise 3. The Hole Argument 4. An Argument from Classical Spacetime Theory 5. The Hole Argument Revisited

Maxwell-Huygens, Newton-Cartan, and Saunders-Knox Space-Times

I address a question recently raised by Simon Saunders concerning the relationship between the space-time structure of Newton-Cartan theory and that of what I will call “Maxwell-Huygens space-time.” This discussion will also clarify a connection between Saunders’s work and a recent paper by Eleanor Knox.

Inertial motion, explanation, and the foundations of classical spacetime theories

I begin by reviewing some recent work on the status of the geodesic principle in general relativity and the geometrized formulation of Newtonian gravitation. I then turn to the question of whether either of these theories might be said to “explain” inertial motion. I argue that there is a sense in which both theories may be understood to explain inertial motion, but that the sense of “explain” is rather different from what one might have expected. This sense of explanation is connected with a view of theories—I call it the “puzzleball view”—on which the foundations of a physical theory are best understood as a network of mutually interdependent principles and assumptions.

A Brief Remark on Energy Conditions and the Geroch-Jang Theorem

The status of the geodesic principle in General Relativity has been a topic of some interest in the recent literature on the foundations of spacetime theories. Part of this discussion has focused on the role that a certain energy condition plays in the proof of a theorem due to Bob Geroch and Pong-Soo Jang [“Motion of a Body in General Relativity.” Journal of Mathematical Physics16(1) (1975)] that can be taken to make precise the claim that the geodesic principle is a theorem, rather than a postulate, of General Relativity. In this brief note, I show, by explicit counterexample, that not only is a weaker energy condition than the one Geroch and Jang state insufficient to prove the theorem, but in fact a condition still stronger than the one that they assume is necessary.

Fiber bundles, Yang–Mills theory, and general relativity

I articulate and discuss a geometrical interpretation of Yang–Mills theory. Analogies and disanalogies between Yang–Mills theory and general relativity are also considered.

On Gravitational Energy in Newtonian Theories

There are well-known problems associated with the idea of (local) gravitational energy in general relativity. We offer a new perspective on those problems by comparison with Newtonian gravitation, and particularly geometrized Newtonian gravitation (i.e., Newton–Cartan theory). We show that there is a natural candidate for the energy density of a Newtonian gravitational field. But we observe that this quantity is gauge dependent, and that it cannot be defined in the geometrized (gauge-free) theory without introducing further structure. We then address a potential response by showing that there is an analogue to the Weyl tensor in geometrized Newtonian gravitation.

The Geometry of Conventionality

There is a venerable position in the philosophy of space and time that holds that the geometry of spacetime is conventional, provided one is willing to postulate a “universal force field.” Here we ask a more focused question, inspired by this literature: in the context of our best classical theories of space and time, if one understands “force” in the standard way, can one accommodate different geometries by postulating a new force field? We argue that the answer depends on one’s theory. In Newtonian gravitation the answer is yes; in relativity theory, it is no.

What Is a Singularity in Geometrized Newtonian Gravitation

I discuss singular space-times in the context of the geometrized formulation of Newtonian gravitation. I argue first that geodesic incompleteness is a natural criterion for when a model of geometrized Newtonian gravitation is singular, and then I show that singularities in this sense arise naturally in classical physics by stating and proving a classical version of the Raychaudhuri-Komar singularity theorem.

Index of refraction engineering in five-level dressed interacting ground states atoms.

We present a five-level atomic system in which the index of refraction of a probe laser can be enhanced or reduced below unity with vanishing absorption in the region between pairs of absorption and gain lines formed by dressing of the atoms with a control laser and rf/microwave fields. By weak incoherent pumping of the population into a single metastable state, one can create several narrow amplifying resonances. At frequencies between these gain lines and additional absorption lines, there exist regions of vanishing absorption but resonantly enhanced index of refraction. In Rb vapors with density N in units of cm(-3), we predict an index of refraction up to n≈√(1+1.2×10(-14)N) for the D1 line, which is more than an order of magnitude larger than other proposals for index of refraction enhancement. Furthermore, the index can be readily reduced below 1 by simply changing the sign of the probe or rf field detunings. This enhancement is robust with respect to homogeneous and inhomogeneous broadening.